We can get there from here

I was in a conversation at Fermilab yesterday when I first heard
about it. “Is that like one of those things where astrophysicists
say that quasar jets travel faster than light, but only because
they’re leaving out some projection effect?” I said.

“No, this is for real. Except— I think so. I can’t really tell;
the article doesn’t say very much.”

I shrugged. I have no nose for news. It was only when my wife
asked me about it that I knew it was a big story. She usually hears
too much physics from me, so she doesn’t actively seek it out. By
that point, it was in all the newspapers, the experimenters
made their paper public,
and CERN’s director general sent out a general e-mail.

If it’s true that neutrinos travel faster than light, it would be a
huge upset. Some may take it to mean that relativity is overturned,
Einstein rolls in his grave, and there’s no longer any limitation on
the speed of future spaceships: we can get to distant stars in
weeks, rather than decades. However, the implications run a lot
deeper than that.

Relativity is a fact of life, as much as falling or heat and cold.
We may not experience relativity in everyday things, but particle
physicists encounter it daily. It’s not a small effect, something
that might be a mirage. In fact, in the conversation at Fermilab I
was learning about special techniques to measure particles that
travel significantly slower than the speed of
light: those are the oddballs. If this new observation about
neutrinos is true, then it would have to fit into the constant
stream of other observations. The new data would have to augment relativity—
they can’t overturn it.

Relativity is about rotation. Unlike rotating a picture frame,
which mixes one space dimension (the horizontal) with another (the
vertical), relativity is about rotations that mix a space dimension
with time. Time is a dimension very much like length, width, and
height, but with a minus sign in the mathematical expressions that
makes a big difference. Distances and time intervals can be
measured in the same units: an inch of time is 85 picoseconds, and a
minute of length is about 11 million miles. A handy unit to
remember is that a foot is one nanosecond.

We can draw time and space in a single plot— I drew an example
below. Looking at plots like this is a bit like viewing time on its
side. Everything that has any duration, like a human life, becomes
a tall, thin strand: we’re about six feet from head to foot, but
three quintillion nanoseconds (95 years) from birth to death. If I
drew everything on the plot, all of the streaks of stars and
spaghetti of intersecting human lives, we wouldn’t be able to see
anything, so I just drew one little spaceship. It enters the frame
at a constant speed from the bottom, then slows to a stop at the
point. The speed of the spaceship is distance-per-time: the
steepness of the slope of its path. Speed is an angle.

Relativity is about rotations in space and time, which is to say,
changing speed. Whenever you change your speed, you rotate yourself
in space and time. This “mixes” space with
time: you convert a little bit of what had been time into space, and
what had been space into time. To explain what I mean by this
mixing, below is an example of a space-space rotation. If we tilt a
hanging picture, the picture’s horizontal line becomes partly
horizontal and partly vertical. There’s nothing magic about that:
it’s just a matter of how one defines horizontal and vertical.

Space-time doesn’t work exactly like that, because if we rotated
180 degrees, we could reverse time! The minus sign in the
mathematical expression for space-time rotations changes the picture
to the one below. This is what the space-time plot
would look like to someone at a different space-time angle, that is
to say, a different speed.

The time and distance axes slant toward each other, and all paths
squish and stretch in between. At an extreme, if we rotate toward
the speed of light, the time axis and distance axis get closer and
closer to overlapping. Light itself inhabits a strange world in
which there is no difference between space and time.

This mixing of space and time is only noticeable at high speeds,
close to the speed of light. However, there’s no boundary line:
it’s always happening to some small degree. For instance, if you
walk toward the Andromeda Galaxy on a Wednesday, then it becomes
next Saturday in Andromeda. If you then turn and walk away from it,
it becomes last Sunday in Andromeda. Your space-time angle is very
small at normal walking speeds, but the axis from here to Andromeda
is long enough to easily shift it by a week.

The experiment that seems to show particles moving faster than
light is a collaboration between the European Laboratory CERN and
the Italian Laboratory of Gran Sasso in the Alps. CERN sends a beam
of neutrinos from its accelerator complex in Geneva, Switzerland to
Gran Sasso’s underground (technically, under-mountain) laboratory,
450 miles away. Neutrinos pass through miles of rock without even
noticing— they interact so weakly that they are effectively
ghosts. In Gran Sasso, there is a large neutrino detector called
Opera; the reason it is large is to improve the chances of detecting some of the
few neutrino interactions. Although the main purpose of the
experiment is to study the way that neutrinos of one type change
into another, they also measured the time of the neutrinos’ flight
and the distance between the labs very precisely in order to
determine their speed. There are some alternate theories of
neutrino transformation and some theories of quantum gravity that
predict that the neutrinos would slow down in various ways. But
instead, they observed the neutrinos traveling faster than
expected, and faster than light.

There’s nothing in the theory of relativity that forbids
faster-than-light particles. Their mass would be an imaginary
number (i.e. mass-squared is a negative number), but that’s just
strange, not forbidden. For neutrinos in particular, however, we know from
previous experiments that they have non-imaginary mass differences.
That would have to be reconciled somehow. If imaginary-mass
particles exist, then they would never be able to go slower than the
speed of light— such things were called tachyons when theorists
played with the idea in string theory. The problem with
faster-than-light particles is a philosophical one: they can tell us
the future.

Taking the Gran Sasso measurement as a case-in-point, Gran Sasso is
2.4 million nanoseconds distant from CERN (450 miles), and they
measured the neutrinos arriving 2.4 million minus 60 nanoseconds
after they left CERN. These measurements were all made by
stationary clocks (with the exception of a satellite, but it was
calibrated for Earth-time). From our perspective, the neutrinos appear to be slightly
faster than light, but from a different perspective, an observer
traveling at relativistic speeds, they would be much faster
than light, or even happen in the wrong order: Gran Sasso receives
the neutrinos before CERN sends them. This is just what happens
when you apply normal relativistic rotations to particles traveling
faster than light. For an observer traveling at 99.999999992% of
the speed of light, the timing of “CERN-emits” and “Gran
Sasso-receives” can be completely reversed, so that “CERN-emits”
happens 2.4 million minus 60 nanoseconds after “Gran
Sasso-receives.” This is not an incredibly high speed: a proton
with 80 TeV of energy (a little more than ten times the LHC’s design
energy) would be going that fast. Faster-than-light travel is not a
different thing from time-travel— if you have one, you the other.

Now imagine that the high-speed observer can emit neutrinos. As
he passes by Gran Sasso, he sends neutrinos to CERN if Gran Sasso
received neutrinos from CERN. If CERN gets neutrinos, they choose
not to send neutrinos to Gran Sasso. Now neutrinos only get sent
around if they don’t get sent around: a paradox!

If this faster-than-light thing stands up to scrutiny, you know this
is the first thing we’ll try to do. You just know it is.

So what about that measurement? Can we believe it? There’s a
strong temptation to pull something out of the procedure and say,
“This part must be wrong; the whole thing is crap,” but after
reading their paper and listening to the spokesperson’s presentation
and response to questions, I don’t see any obvious faults. They
took it very seriously and measured nearly all steps in the chain
multiple times in multiple ways. There’s another strong temptation
to say, “Gee wiz, time travel!” but that would be jumping way
ahead of the facts. It takes time to confirm an observation, to
find the same thing emerge in so many different ways that it must be
true. I want to believe it or disbelieve it: I hate suspense! The
hardest part of science is the ache of uncertainty.

The first caveat in the experiment is that the initial time of each
neutrino is not known. When I heard about this experiment, I
imagined someone starting a clock at the instant that the neutrino
was produced at CERN and someone stopping a clock when it was
received in Gran Sasso. Not quite. In order to make large batches
of neutrinos (in the hopes that a few will be seen), they are
produced in long bursts from the accelerator, about 10 thousand
nanoseconds from start to finish. The neutrino that is detected in
Gran Sasso might be from the start of the burst, the end of the
burst, or anywhere in between. How, then, could they have possibly
measured a 60 nanosecond difference in arrival time?

They accumulated a large number of neutrinos (16 thousand) and
statistically fitted the distribution. CERN measured the shape of
the burst, the Opera detector cataloged the arrival times of all the
neutrinos, and the analysis team varied the time-offset between the
shape and the observed distribution until they fit. Here’s what
that looks like (copied
from their paper):

The start-time of any one neutrino is unknown, but you can learn
what you need to from a distribution of all of them. This is
standard practice in particle physics, especially where the
uncertainties of quantum mechanics play a role. It looks like a
good fit, but the relevant scale is 60 nanoseconds, while the
horizontal axis covers 10 thousand nanoseconds. They provide a
close-up of the leading and trailing edges, which are the most
important parts of the fit:

The other caveat about the measurement is that it could not be
performed by a single clock. There must be at least two clocks: one
at CERN and the other at Gran Sasso, and they need to be
synchronized. But the experiment is in a hard-to-reach location, so
a long series of clocks is needed, including a satellite link. Even
something as mundane as cabling could ruin the measurement:
electronics signals pass through cables close to the speed of light,
which is 60 nanoseconds = 60 extra feet of cables. The electronics
themselves needed to be carefully calibrated, since signals pass
more slowly through computers than wires. The distance also had to
be surveyed through all the tunnels that lead down to the
underground experiment. The surveying operation was complicated by
the fact that they could only close one lane of traffic.

The only way to know if there isn’t an error somewhere in the chain
is to cross-check each step carefully. I got the impression from
the spokesperson that a lot of different techniques were used to do
all of this double-checking, and there were naturally a lot of
questions about each part. The number of reviewers has just
increased dramatically, but we need to wait to see if someone finds
something.

Even though I can’t say that I know the result is wrong, I have a
strong suspicion that neutrinos do not travel faster than light. My
personal bias is based on the philosophical paradox that would be
raised if anything could travel faster than light.

Suppose that closer investigation reveals some error, or that
follow-up experiments do not find any faster-than-light neutrinos.
This sort of thing has happened before. Would that be a
disappointment? I bet most of the excitement over this result is
the expectation that it would make a Star Trek future possible: it’s
a bummer that stars are so far away, especially the ones with the
most interesting aliens. I mean it.
Many science fiction universes have some kind of
faster-than-light travel for good reason.